Show simple item record

dc.contributor.authorPitts, JB
dc.date.accessioned2015-03-16T11:21:56Z
dc.date.available2015-03-16T11:21:56Z
dc.date.issued2014
dc.identifier.citationAnnals of Physics Volume 351, December 2014, Pages 382–406. DOI: 10.1016/j.aop.2014.08.014
dc.identifier.issn0003-4916
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/247013
dc.description.abstractIn Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. Each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary gradient, spoiling Gauss's law. The secondary constraint p^i,_i=0 still holds, but being a function of derivatives of momenta (mere auxiliary fields), it is not directly about the observable electric field (a function of derivatives of A), which couples to charge. Only a special combination of the two first-class constraints, the Anderson-Bergmann-Castellani gauge generator G, leaves E unchanged. Likewise only that combination leaves the canonical action invariant---an argument independent of observables. If one uses a first-class constraint to generate instead a canonical transformation, one partly strips the canonical coordinates of physical meaning as electromagnetic potentials, vindicating the Anderson-Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant q,t-dH/dp=-E-p=0 supports using the gauge generator and primary Hamiltonian rather than the separate first-class constraints and the extended Hamiltonian. Partly paralleling Pons's criticism, it is shown that Dirac's proof that a first-class primary constraint generates a gauge transformation, by comparing evolutions from _identical_ initial data, cancels out and hence fails to detect the alterations made to the initial state. It also neglects the arbitrary coordinates multiplying the secondary constraints _inside_ the canonical Hamiltonian. Thus the gauge-generating property has been ascribed to the primaries alone. Hence the Dirac conjecture about secondary first-class constraints as generating gauge transformations rests upon a false presupposition about primary first-class constraints. Clarity about electromagnetism help with GR.
dc.languageEnglish
dc.language.isoen
dc.publisherElsevier BV
dc.subjectDirac-Bergmann constrained dynamics
dc.subjectgauge transformations
dc.subjectcanonical quantization
dc.subjectobservables
dc.subjectHamiltonian methods
dc.subjectfirst-class constraints
dc.subjectproblem of time
dc.titleA first class constraint generates not a gauge transformation, but a bad physical change: The case of electromagnetism
dc.typeArticle
dc.description.versionThis is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0003491614002504.
prism.endingPage406
prism.publicationDate2014
prism.publicationNameAnnals of Physics
prism.startingPage382
prism.volume351
rioxxterms.versionofrecord10.1016/j.aop.2014.08.014
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2014-09-06
dc.contributor.orcidPitts, Brian [0000-0002-7299-5137]
dc.identifier.eissn1096-035X
dc.publisher.urlhttp://dx.doi.org/10.1016/j.aop.2014.08.014
rioxxterms.typeJournal Article/Review
rioxxterms.freetoread.startdate2015-09-06


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record